Problem: Solve for $x$ and $y$ using elimination. ${4x+y = 43}$ ${-5x-y = -52}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {4x+y = 43}\thinspace$ to find $y$ ${4}{(9)}{ + y = 43}$ $36+y = 43$ $36{-36} + y = 43{-36}$ ${y = 7}$ You can also plug ${x = 9}$ into $\thinspace {-5x-y = -52}\thinspace$ and get the same answer for $y$ : ${-5}{(9)}{ - y = -52}$ ${y = 7}$